Lipman Bers

Lipman Bers (Latvian: Lipmans Berss; May 22, 1914 – October 29, 1993) was a Latvian-American mathematician, born in Riga, who created the theory of pseudoanalytic functions and worked on Riemann surfaces and Kleinian groups. He was also known for his work in human rights activism.

Bers was born in Riga, then under the rule of the Russian Czars, and spent several years as a child in Saint Petersburg; his family returned to Riga in approximately 1919, by which time it was part of independent Latvia. In Riga, his mother was the principal of a Jewish elementary school, and his father became the principal of a Jewish high school, both of which Bers attended, with an interlude in Berlin while his mother, by then separated from his father, attended the Berlin Psychoanalytic Institute. After high school, Bers studied at the University of Zurich for a year, but had to return to Riga again because of the difficulty of transferring money from Latvia in the international financial crisis of the time. He continued his studies at the University of Riga, where he became active in socialist politics, including giving political speeches and working for an underground newspaper. In the aftermath of the Latvian coup in 1934 by right-wing leader Kārlis Ulmanis, Bers was targeted for arrest but fled the country, first to Estonia and then to Czechoslovakia.

Bers received his Ph.D. in 1938 from the University of Prague. He had begun his studies in Prague with Rudolf Carnap, but when Carnap moved to the US he switched to Charles Loewner, who would eventually become his thesis advisor. In Prague, he lived with an aunt, and married his wife Mary (née Kagan) whom he had met in elementary school and who had followed him from Riga. Having applied for postdoctoral studies in Paris, he was given a visa to go to France soon after the Munich Agreement, by which Nazi Germany annexed the Sudetenland. He and his wife Mary had a daughter in Paris. They were unable to obtain a visa there to emigrate to the US, as the Latvian quota had filled, so they escaped to the south of France ten days before the fall of Paris, and eventually obtained an emergency US visa in Marseilles, one of a group of 10,000 visas set aside for political refugees by Eleanor Roosevelt. The Bers family rejoined Bers' mother, who had by then moved to New York City and become a psychoanalyst, married to thespian Beno Tumarin. At this time, Bers worked for the YIVO Yiddish research agency.

Bers spent World War II teaching mathematics as a research associate at Brown University, where he was joined by Loewner. After the war, Bers found an assistant professorship at Syracuse University (1945–1951), before moving to New York University (1951–1964) and then Columbia University (1964–1982), where he became the Davies Professor of Mathematics, and where he chaired the mathematics department from 1972 to 1975. His move to NYU coincided with a move of his family to New Rochelle, New York, where he joined a small community of émigré mathematicians. He was a visiting scholar at the Institute for Advanced Study in 1949–51. He was a Vice-President (1963–65) and a President (1975–77) of the American Mathematical Society, chaired the Division of Mathematical Sciences of the United States National Research Council from 1969 to 1971, chaired the U.S. National Committee on Mathematics from 1977 to 1981, and chaired the Mathematics Section of the National Academy of Sciences from 1967 to 1970.

Late in his life, Bers suffered from Parkinson's disease and strokes. He died on October 29, 1993.

Bers' doctoral work was on the subject of potential theory. While in Paris, he worked on Green's function and on integral representations. After first moving to the US, while working for YIVO, he researched Yiddish mathematics textbooks rather than pure mathematics.

At Brown, he began working on problems of fluid dynamics, and in particular on the two-dimensional subsonic flows associated with cross-sections of airfoils. At this time, he began his work with Abe Gelbart on what would eventually develop into the theory of pseudoanalytic functions. Through the 1940s and 1950s he continued to develop this theory, and to use it to study the planar elliptic partial differential equations associated with subsonic flows. Another of his major results in this time concerned the singularities of the partial differential equations defining minimal surfaces. Bers proved an extension of Riemann's theorem on removable singularities, showing that any isolated singularity of a pencil of minimal surfaces can be removed; he spoke on this result at the 1950 International Congress of Mathematicians and published it in Annals of Mathematics.

Later, beginning with his visit to the Institute for Advanced Study, Bers "began a ten-year odyssey that took him from pseudoanalytic functions and elliptic equations to quasiconformal mappings, Teichmüller theory, and Kleinian groups". With Lars Ahlfors, he solved the "moduli problem", of finding a holomorphic parameterization of the Teichmüller space, each point of which represents a compact Riemann surface of a given genus. During this period he also coined the popular phrasing of a question on eigenvalues of planar domains, "Can one hear the shape of a drum?", used as an article title by Mark Kac in 1966 and finally answered negatively in 1992 by an academic descendant of Bers. In the late 1950s, by way of adding a coda to his earlier work, Bers wrote several major retrospectives of flows, pseudoanalytic functions, fixed point methods, Riemann surface theory prior to his work on moduli, and the theory of several complex variables. In 1958, he presented his work on Riemann surfaces in a second talk at the International Congress of Mathematicians.